If a baby is mistakenly switched at birth in the hospital (it has been known to happen) and later (i.e. 5, 10, or 15 years later) the mistake is realized, what is the halacha? Do the parents that brought up the child have any rights, or do the real parents have all the rights to the child?

Popa, if we are talking about switched and not snatched, then we have to see if it was an even trade. If it was a boy for girl, would they have to pay back the ones who raised their boy without getting help? If we find out during Shiduchim, can you charge more Nadden for the new Yichus?

There’s a story in yesterday’s Washington Post “WHO WAS SHE? A DNA TEST ONLY OPENED NEW MYSTERIES” describing how until almost the second half of the 20th century hospitals in NYC and in America weren’t very good at correctly identifying newborns and sending them home with the correct parents. The article focuses on an Irish woman who just for the fun of it did a DNA test and found out that her “Irish” grandfather, born in Manhattan, was in fact an Ashkenazic Jew. His Irish parents were given the wrong baby while the Jewish parents took him the Irish baby. No one realized this mistake until a hundred years later when she did this DNA test. Both babies were born the same day at the same hospital using the same doctor and it turned out their birth certificates were one number apart from each other.

From a halachic perspective, do we say the child brought up as Irish is Jewish and the one brought up as Jewish is non-Jewish? If they had been female, would that have affected the respective Jewish-status of their offspring, even though the error only came to light 100 years later?

It is Assur for them to remain together. They must divorce. Any children they had together are Challalim (their sons are not Kohanim, and their daughters may not marry Kohanim).
A good friend of mine is a Challal for exactly this reason (no DNA test involved, but it was a case of accidentally violating the Halacha).

One common thread in almost all switched at birth stories is the mother almost always is insisting that this is not her baby and her concerns are not taken seriously. I’ve read several such stories and in pretty much every case the mother knew. One such mother had been protesting for days that she was sent home with the wrong baby and when no one was taking her seriously she started staying quiet and not telling anyone. As her daughter got older and it became more obvious that this child looked nothing like her other children, she was certain that this was someone else’s child and started writing letters to the daughter that was being raised by someone else and putting them in a drawer for when she would eventually hopefully meet her daughter again. She never said anything until her dying day because she didn’t want the daughter she was raising to feel “less than” her other children. Unfortunately the switch wasn’t proven until after the mother’s death.

Joseph, I don’t remember the exact details; his father was a Ba’al Teshuva, and I think his mother was a Giyores. Presumably, his father subsequently found out that he was a Kohen.

Laskern, yes, they would be. I don’t believe there is any question about this. (There was a debate among the Poskim about fifty years ago regarding the status a child from artificial insemination using donor sperm. Rav Moshe Feinstein ruled that he is not a Mamzer because the Mamzeirus status depends on a מעשה ביאה).

Its almost unimaginable, but what if someone could show that Joseph was switched at birth and his real parents were an MO couple from San Francisco who graduated from UC Berkley, were active in Democratic Party politics and now own the only Canabis dispensary w Chasidishe hashgacha???

Joseph; I read that story. I don’t know enough details as to the actual birth to know whether or not the women protested or if it was even possible for them to be aware of the switch. If I recall correctly, at that time women were often put to sleep and then given their baby when they woke up, which could easily have been the wrong baby to begin with.